What is the inverse of (x+3)/(4x^2+3x-2) ?

The inverse of (x+3)/(4x^2+3x-2) is (-3x+1+sqrt(41x^2+42x+1))/(8x),(-3x+1-sqrt(41x^2+42x+1))/(8x)

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inverse of (x+3)/(4x^2+3x-2)

inverse

\frac{x + 3}{4 x ^{2} + 3 x - 2}

\frac{- 3 x + 1 + 41 x ^{2} + 42 x + 1}{8 x}, \frac{- 3 x + 1 - 41 x ^{2} + 42 x + 1}{8 x}

Solution steps

y = \frac{x + 3}{4 x ^{2} + 3 x - 2}

Replace

x

with

y

x = \frac{y + 3}{4 y ^{2} + 3 y - 2}

Solve for

y, x = \frac{y + 3}{4 y ^{2} + 3 y - 2}

\frac{- 3 x + 1 + 41 x ^{2} + 42 x + 1}{8 x}, \frac{- 3 x + 1 - 41 x ^{2} + 42 x + 1}{8 x}

f (x) = 0.09 x + 17 + \frac{350}{x}

\frac{( 7 + \frac{1}{x} )}{( \frac{1}{x} )}

(- 5, - 5), (- 9, - 2)

f (x) = (x - 5)^{\frac{4}{5}}

f (x) = 5 - x + 6 + x

What is the inverse of (x+3)/(4x^2+3x-2) ?
The inverse of (x+3)/(4x^2+3x-2) is (-3x+1+sqrt(41x^2+42x+1))/(8x),(-3x+1-sqrt(41x^2+42x+1))/(8x)